Sent out to encourage savings (4,3)
I believe the answer is:
nest egg
'savings' is the definition.
(nest egg can mean someone's savings)
'sent out to encourage' is the wordplay.
'out' indicates an anagram (out can mean wrong or inaccurate).
'to encourage' becomes 'egg'.
'sent' is an anagram of 'nest'.
'nest'+'egg'='NEST-EGG'
(Other definitions for nest egg that I've seen before include "Money saved for the future" , "Saved-up money" , "Money kept in reserve" , "Reserve funds" , "Rainy day savings" .)